Temporal structure of aggregate power fluctuations in large-eddy simulations of extended wind-farms

Fluctuations represent a major challenge for the incorporation of electric power from large wind-farms into power grids. Wind farm power output fluctuates strongly in time, over various time scales. Understanding these fluctuations, especially their spatio-temporal characteristics, is particularly important for the design of backup power systems that must be readily available in conjunction with wind-farms. In this work we analyze the power fluctuations associated with the wind-input variability at scales between minutes to several hours, using large eddy simulations (LES) of extended wind-parks, interacting with the atmospheric boundary layer. LES studies enable careful control of parameters and availability of wind-velocities simultaneously across the entire wind-farm. The present study focuses on neutral atmospheric conditions and flat terrain, using actuator-disk representations of the individual wind-turbines. We consider power from various aggregates of wind-turbines such as the total average power signal, or signals from sub-averages within the wind-farm. Non-trivial correlations are observed due to the complex interactions between turbines placed downstream of each other, and they lead to noticeable spectral peaks at frequencies associated with the inter-turbine spacings when the wind-direction is completely fixed. In that case we observe that the frequency spectra of the total wind-farm output show a decay that follows approximately a $-5/3$ power-law scaling regime, qualitatively consistent with some observations made in field-scale operational wind-parks (Apt, 2007). We find that these features are still observed when the wind-speed varies in magnitude. However, significant changes in the wind-direction over time tend to smooth out the observed spectral peak and reduce the extent of the observed $-5/3$ power-law.